The primary reason that you can assign to $null - even though as the representation of a null value it should be constant (as other PowerShell automatic variables such as $true and $false are, for instance) - is that it enables the following useful idiom for output suppression:
# Discard the success output from a command.
$null = Get-Item -ErrorAction Stop foo.txt
That is, $null can act like a regular read-write variable that you can assign to, but whatever you assign to it (a command's success output, from stream number 1 - see about_Redirection) is quietly discarded.
Effectively, $null = ... is the equivalent of >NUL (1>NUL) in cmd.exe and >/dev/null (1>/dev/null) in POSIX-compatible shells such as bash.
Note that in PowerShell you could alternatively use ... | Out-Null or > $null, though the $null = ... idiom is faster than Out-Null[1] and also signals the intent to discard the (success) output up front (unlike > $null). (There's also [void] (...), but it requires you to enclose the command in parentheses.) See this answer for more.
However, you do need redirection if you also want to suppress other output streams (too); e.g.,
*> $null discards the output from all streams.
As for inspecting the properties of variables, including automatic ones, use the Get-Variable cmdlet and pass it the name of the variable without the $ sigil; e.g., null to inspect $null.
PS> Get-Variable null | Format-List
Value :
Description : References to the null variable always return the null value. Assignments have no effect.
Options : None
Name : null
Visibility : Public
Module :
ModuleName :
Attributes : {}
Format-List * ensures that that all properties of the variable object (a System.Management.Automation.PSVariable instance or an instance of a derived class) are listed, in list form.
A constant variable such as $false would show Constant as part of the Options property value.
[1] Note: PowerShell [Core] v6+ has an optimization that makes Out-Null the fastest solution if you discard an expression's value (e.g., 1..1e6 | Out-Null vs. a command's (e.g., Write-Output (1..1e6) | Out-Null), but note that suppressing command output is the much more common use case.